Question

How much work is done by pressure in forcing $\mathbf{1}\mathbf{.}\mathbf{4}\mathbf{}{\mathbf{m}}^{\mathbf{3}}$of water through a pipe having an internal diameter of $13\mathrm{mm}$if the difference in pressure at the two ends of the pipe is $1.0\mathrm{atm}$?

Short answer

Work done by pressure to force the water through a pipe is $1.4\times {10}^5\mathrm{J}$.

Step-by-step solution

Given information

• The volume of water flowing through the pipe is$\mathrm{V}=1.4{\mathrm{m}}^3$

• The pressure difference between two ends of the pipe is

$∆\mathrm{\rho }=1.0\mathrm{atm}$

$=1.01\times {10}^5\mathrm{Pa}$

Determining the concept of work done

The work done is the product of force and displacement. It can also be written in terms of change in pressure and volume.

Using the formula for work done, find the work done by pressure to force the water through the pipe.

The formula is as follows:

$\mathrm{W}=\mathrm{pv}$

where, $\mathrm{W}$is work done, $\mathrm{p}$is pressure and$\mathrm{V}$is volume.

Determining the work done by pressure to force the water through the pipe

The equation for work done can be written as,

$\mathrm{W}=\mathrm{p}\times \mathrm{v}$

Here, the volume of water remains constant, and only pressure changes. So,

$\mathrm{Wp}=\mathrm{v}$

Substituting the given values,

$\mathrm{W}=(1.01\times {10}^5\mathrm{Pa})\times 1.4{\mathrm{m}}^3$

$=1.4\times {10}^5\mathrm{J}$

Hence, work done by pressure to force the water through pipe is $1.4\times {10}^5\mathrm{J}$.